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Extended eigenvalues and the Volterra operator

Published online by Cambridge University Press:  26 February 2003

Animikh Biswas ,
Alan Lambert  and
Srdjan Petrovic
Animikh Biswas
Affiliation:
9201 University City Blvd, Department of Mathematics, UNC Charlotte, Charlotte, NC 28223, USA e-mail: abiswas@uncc.edu and allamber@email.uncc.edu
Alan Lambert
Affiliation:
9201 University City Blvd, Department of Mathematics, UNC Charlotte, Charlotte, NC 28223, USA e-mail: abiswas@uncc.edu and allamber@email.uncc.edu
Srdjan Petrovic
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA e-mail: srdjan.petrovic@wmich.edu
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In this paper we consider the integral Volterra operator on the space L^2(0,1). We say that a complex number \lambda is an extended eigenvalue ofV if there exists a nonzero operator X satisfying the equation XV=\lambda VX. We show that the set of extended eigenvalues of V is precisely the interval (0,\infty ) and the corresponding eigenvectors may be chosen to be integral operators as well.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 521 - 534
Copyright
2002 Glasgow Mathematical Journal Trust